Dempsey, 30, only joined Spurs last summer after five years at Fulham and, after a slow start, became a more regular fixture in Andre Villas-Boas’s first team.
Spurs confirmed the news in a brief statement, adding: "We wish Clint every success for the future."
After the success of the David Beckham experiment, American clubs are keen to bring players over from Europe while they are still somewhere near their prime, as opposed to at the end of their careers.
It is a major coup for Seattle, whose squad boasts Dempsey’s former Fulham team-mate Eddie Johnson.
There is also a spare designated player slot at Seattle, after Shalrie Joseph's contract was restructured to allow the team sign another marquee signing in addition to Obafemi Martins and Mauro Rosales.
The US reports claim Seattle would offer Dempsey $8 million (£5.2m) for four years - giving him the highest base salary in the league's history - and allow him off-season loans to European clubs in order to keep him fresh for the US national team.
- Sports & Recreation